Emulating Type Families in Rust

Rust's powerful trait system allows for significant compile-time metaprogramming. However, it lacks direct support for "type families" as found in languages like Haskell, which are a way to associate types with other types based on a type parameter. This challenge asks you to implement a system that mimics this behavior using Rust's existing features.

Problem Description

Your task is to create a Rust system that allows you to define a mapping from a given type to another type. This mapping should be resolved at compile time. You'll need to define traits and potentially helper structs or enums to achieve this. The goal is to create a mechanism where, given a "key" type, you can retrieve a corresponding "value" type.

Key Requirements:

• Compile-time Resolution: The mapping must be determined entirely at compile time. No runtime lookups should be involved.
• Generic Key Type: The mapping should be able to use any type as a "key".
• Generic Value Type: The mapped types (the "values") can also be any valid Rust types.
• Extensibility: It should be straightforward to add new mappings to your system.
• Compile-time Errors for Unmapped Types: If a key type is provided for which no mapping has been defined, the compiler should issue an error.

Expected Behavior:

You should be able to define a set of mappings. Then, you should be able to use these mappings in generic functions or structs to constrain or determine types.

Examples

Example 1: Simple Integer to String Mapping

Let's say we want to map i32 to String and u64 to String.

// Assume you have defined your type family mechanism (e.g., a trait `TypeFamily`)
// and registered your mappings.

// Hypothetical usage:
// type MappedType = <MyTypeFamily as TypeFamily<InputType>>::AssociatedType;

// If InputType is i32, MappedType should resolve to String.
// If InputType is u64, MappedType should resolve to String.
// If InputType is f32, compilation should fail because there's no mapping.

fn process_mapped<T>() {
    // This function needs to know the mapped type of T at compile time.
    // For instance, to create a default value of the mapped type.
    type AssociatedType = <YourTypeFamilyImpl as TypeFamily<T>>::AssociatedType;

    // Example of using the associated type:
    let _default_value: AssociatedType = Default::default();
    println!("Successfully resolved and used associated type.");
}

// You would then call this function with concrete types:
// process_mapped::<i32>(); // Should compile
// process_mapped::<u64>(); // Should compile
// process_mapped::<f32>(); // Should NOT compile

Example 2: Mapping to Different Types

Consider mapping a struct to a different struct.

struct UserData { /* ... */ }
struct UserProfile { /* ... */ }

struct AdminData { /* ... */ }
struct AdminProfile { /* ... */ }

// Assume these types are mapped:
// UserData -> UserProfile
// AdminData -> AdminProfile

// Hypothetical usage in a generic function:
fn generate_profile<T>() -> <YourTypeFamilyImpl as TypeFamily<T>>::AssociatedType {
    // ... logic to construct the profile ...
    unimplemented!() // Placeholder
}

// Calling the function:
// let user_profile: UserProfile = generate_profile::<UserData>(); // Should compile
// let admin_profile: AdminProfile = generate_profile::<AdminData>(); // Should compile

Example 3: Edge Case - No Mapping Defined

If you attempt to use a type that has no mapping defined, compilation should fail.

struct UnmappedType;

// Attempting to resolve the type family for UnmappedType:
// type ResultType = <YourTypeFamilyImpl as TypeFamily<UnmappedType>>::AssociatedType;
// This line should produce a compile-time error.

Constraints

• Rust Edition: Use the latest stable Rust edition.
• No External Crates for Core Logic: You may use helper crates if absolutely necessary for general utilities, but the core type family emulation mechanism should be built using standard Rust features (traits, generics, associated types, macros).
• Compile-time Performance: While not strictly enforced with a timer, the solution should not have significantly worse compile times than a reasonably complex generic Rust program. Avoid overly complex macro expansions that lead to extreme compilation bottlenecks.
• Clarity and Idiomatic Rust: The solution should be understandable and follow common Rust patterns.

Notes

• Associated Types: Consider how associated types within traits can be used to represent the "mapped" type.
• Trait Implementations: Think about how you can define individual trait implementations to create specific mappings.
• Macros: Macros are likely to be your most powerful tool for defining and managing these mappings in a concise and extensible way. Consider using declarative macros (macro_rules!) or procedural macros.
• "Sealing" Traits: You might want to prevent users from implementing your core type family traits themselves, forcing them to use your defined mapping mechanism. This can be achieved using private traits or other techniques.
• Default Implementations: Consider how you might provide a "default" or "fallback" behavior for types that don't have explicit mappings, or how to explicitly disallow them.
• Naming: Choose descriptive names for your traits and any helper constructs. For instance, a trait named TypeFamily or MapType and a trait bound like T: TypeFamily.